Accurately estimating spacecraft location is of crucial importance for a variety of safety-critical tasks in low-Earth orbit (LEO), including satellite collision avoidance and re-entry. The solar activity largely impacts the physical characteristics of the thermosphere, consequently affecting trajectories of spacecraft in LEO. State-of-the-art models for estimating thermospheric density are either computationally expensive or under-perform during extreme solar activity. Moreover, these models provide single-point solutions, neglecting critical information on the associated uncertainty. In this work we use and compare two methods, Monte Carlo dropout and deep ensembles, to estimate thermospheric total mass density and associated uncertainty. The networks are trained using ground-truth density data from five well-calibrated satellites, using orbital data information, solar and geomagnetic indices as input. The trained models improve for a subset of satellites upon operational solutions, also providing measure of uncertainty in the density estimation.